基于铸体薄片的致密岩心孔隙结构多重分形特征研究
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摘要
基于压汞和核磁共振实验进行了致密岩心孔隙结构分类,提取了不同孔隙结构的铸体薄片并应用PSO多阈值分割算法得到孔隙-骨架二值图。结合孔隙结构的多重分形理论计算了不同孔隙结构的多重分形维数及多重分形谱,分析了多重分形维数与饱和中值压力、平均孔喉半径和核磁T2几何平均值的关系。研究表明:基于多重分维表征方法与压汞、核磁共振等实验具有一致性,不同孔隙结构岩石的多重分形特征各异,物性越差、孔隙结构越复杂,多重分形维数越大;多重分形维数与饱和中值压力成正比,与平均孔喉半径和核磁T2几何平均值成反比;D_(min)与孔隙结构类型及其他孔隙结构表征参数的相关性最强,在缺乏压汞、核磁等实验数据时,基于铸体薄片的多重分形维数为致密岩石孔隙结构的定量表征提供了有利依据。
The pore structure of tight cores is classified based on mercury injection and NMR core analysis,the cast slices of different pore structure are obtained,and two dimensional pore-matrix graphs of the cast slices are obtained by PSO multi-threshold segmentation algorithm. Multifractal dimension and multifractal spectrum of different types of pore structure are calculated based on the multifractal theory of pore structure,and the relationships between multifractal dimension and median saturation pressure,average pore radius and nuclear magnetic T_2 geometric mean. The results show that the pore structure characterization method based on multi-fractal has the same effectiveness as mercury injection method and NMR core analysis method. The multi-fractal characteristics of different types of pore structure are different,and the worse the physical properties of cores,the more complex the pore structure,the greater the multifractal dimension. It is also found that the multi-fractal dimension increases with the increase of median saturation pressure,and decreases with the increase of average pore radius and NMR T_2 geometric mean. Dmin has the strongest correlation with pore structure type and other pore structure characterization parameters,in the absence of mercury penetration and NMR experimental data,the multifractal dimension derived from cast slices can provide a favorable basis for the quantitative characterization of tight rock pore structure.
The pore structure of tight cores is classified based on mercury injection and NMR core analysis,the cast slices of different pore structure are obtained,and two dimensional pore-matrix graphs of the cast slices are obtained by PSO multi-threshold segmentation algorithm. Multifractal dimension and multifractal spectrum of different types of pore structure are calculated based on the multifractal theory of pore structure,and the relationships between multifractal dimension and median saturation pressure,average pore radius and nuclear magnetic T_2 geometric mean. The results show that the pore structure characterization method based on multi-fractal has the same effectiveness as mercury injection method and NMR core analysis method. The multi-fractal characteristics of different types of pore structure are different,and the worse the physical properties of cores,the more complex the pore structure,the greater the multifractal dimension. It is also found that the multi-fractal dimension increases with the increase of median saturation pressure,and decreases with the increase of average pore radius and NMR T_2 geometric mean. Dmin has the strongest correlation with pore structure type and other pore structure characterization parameters,in the absence of mercury penetration and NMR experimental data,the multifractal dimension derived from cast slices can provide a favorable basis for the quantitative characterization of tight rock pore structure.
引文
[1]KATZ A J,THOMPSON A H.Fractal sandstone pores:implications for conductivity and pore formation[J].Physical Review Letters,1985,54(12):1325-1328.
[2]贾芬淑,沈平平,李克文.砂岩孔隙结构的分形特征及应用研究[J].断块油气田,1995,2(1):16-21.JIA Fenshu,SHEN Pingping,LI Kewen.Study on the fractal characteristics of sandstone pore structure and its application[J].Fault-Block Oil and Gas Field,1995,2(1):16-21.
[3]刘松玉,张继文.土中孔隙分布的分形特征研究[J].东南大学学报,1997,27(3):129-132.LIU Songyu,ZHANG Jiwen.Fractal approach to measuring soil porosity[J].Journal of Southeast University,1997,27(3):129-132.
[4]王经洲,郑晓,宛农,等.基于扫描电镜图像分析的菜籽仁饼孔隙结构分形研究[J].农业工程学报,2008,24(3):16-20.WANG Jingzhou,ZHENG Xiao,WAN Nong,et al.Fractal character of the pore structure of dehulled rapeseed cake based on scanning electron microscopy image analysis[J].Transactions of the Chinese Society of Agricultural Engineering,2008,24(3):16-20.
[5]孙军昌,周洪涛,郭和坤,等.复杂储层岩石微观非均质性分形几何描述[J].武汉工业学院学报,2009,28(3):42-46.SUN Junchang,ZHOU Hongtao,GUO Hekun,et al.Characterization of complex rock micro-heterogeneity using fractal geometry[J].Journal of Wuhan Polytechnic University,2009,28(3):42-46.
[6]彭瑞东,杨彦从,鞠杨,等.基于灰度CT图像的岩石孔隙分形维数计算[J].科学通报,2011,56(26):2256-2266.PENG Ruidong,YANG Yancong,JU Yang,et al.Computation of fractal dimension of rock pores based on gray CT images[J].Chinese Science Bulletin,2011,56(26):2256-2266.
[7]葛新民,范宜仁,邓少贵,等.基于分形理论的毛管压力和电阻率指数相关性研究[J].中国石油大学学报(自然科学版),2012,36(4):72-76.GE Xinmin,FAN Yiren,DENG Shaogui,et al.Research on correlation between capillary pressure and resistivity index based on fractal theory[J].Journal of China University of Petroleum(Edition of Natural Science),2012,36(4):72-76.
[8]ABDASSAH D,PERMADI P,SUMANTRI Y,et al.Saturation exponents derived from fractal modeling of thinsections[C].SPE 36978,1996.
[9]唐红瑛,唐仁骐.砂岩岩心孔隙结构分形特征的探讨[J].中国科学技术大学学报,2004,34(s1):69-75.TANG Hongying,TANG Renqi.Study on fractal dimensions of sandstone reservoir rock samples pore structure[J].Journal of University of Science and Technology of China,2004,34(s1):69-75.
[10]唐玮,唐仁骐,白喜俊.分形理论在油层物理学中的应用[J].石油学报,2008,29(1):93-96.TANG Wei,TANG Renqi,BAI Xijun.Application of fractal dimension theory to reservoir physics[J].Acta Petrolei Sinica,2008,29(1):93-96.
[11]ESSEX,CHRISTOPHER,NERENBERG,et al.Fractal dimension:limit capacity or hausdorff dimension?[J].American Journal of Physics,1990,58(10):986-988.
[12]HARGIS C D,BISSONETTE J A,DAVID J L.The behavior of landscape metrics commonly used in the study of habitat fragmentation[J].Landscape Ecology,1998,13(3):167-186.
[13]HARGROVE W W,HOFFMAN F M,SCHWARTZ P M.A fractal landscape realizer for generating synthetic maps[J].Conservation Ecology,2002,6(1):2.
[14]孙霞,吴自勤,黄畇.分形原理及其应用[M].合肥:中国科学技术大学出版社,2003.
[15]PATRICIA Tang,NORA Y K Chew,HAK K Chan,et al.Limitation of determination of surface fractal dimension using N2adsorption isotherms and modified Frenkel-HalseyHill theory[J].Langmuir,2003,19:2632-2638.
[16]BREWER J,DI Girolamo L.Limitations of fractal dimension estimation algorithms with implications for cloud studies[J].Atmospheric Research,2006,82(1/2):433-454.
[17]曹汉强,朱光喜,李旭涛,等.多重分形及其在地形特征分析中的应用[J].北京航空航天大学学报,2004,30(12):1182-1185.CAO Hanqiang,ZHU Guangxi,LI Xutao,et al.Multi-fractal and its application in terrain character analysis[J].Journal of Beijing University of Aeronautics and Astronautics,2004,30(12):1182-1185.
[18]成秋明.非线性成矿预测理论:多重分形奇异性-广义自相似性-分形谱系模型与方法[J].地球科学:中国地质大学学报,2006,31(3):337-348.CHENG Qiuming.Singularity-generalized self-similarityfractal spectrum(3S)models[J].Earth Science:Journal of China University of Geosciences,2006,31(3):337-348.
[19]王志敬,成秋明.P-A分形模型定量度量糜棱岩变形过程中石英微结构的变化[J].地球科学:中国地质大学学报,2006,31(3):361-365.WANG Zhijing,CHENG Qiuming.Characterization of micro-texture of quartz myionite deformation process using fractal P-A model[J].Earth Science:Journal of China University of Geosciences,2006,31(3):361-365.
[20]VAZQUEZ E V,FERREIRO J P,MIRANDA J.Multifractal analysis of pore size distributions as affected by simulated rainfall[J].Vadose Zone Journal,2008,7(2):500-511.
[21]PAZ Ferreiro J,VIDAL Vázquez E.Multifractal analysis of Hg pore size distributions in soils with contrasting structural stability[J].Geoderma,2010,160(1):64-73.
[22]GARCIA Gutierrez C,SAN Jose F.Multifractal analysis of soil micro and macroporosity using digital images obtained with fluorescent dye[J].Geophysical Research Abstracts,2006,8:11094.
[23]SAN Jose Martinez F,MARTIN M A,CANIEGO F J,et al.Multifractal analysis of discretized X-ray CT images for the characterization of soil macropore structures[J].Geoderma,2010,156(1/2):32-42.
[24]ZHOU H,PERFECT E,LU Y Z,et al.Multifractal analysis of grayscale and binary soil thin section images[J].Fractals-Complex Geometry Patterns and Scaling in Nature and Society,2011,19(3):299-309.
[25]JOUINI M S,VEGA S,MOKHTAR E A.Multiscale characterization of pore spaces using multifractals analysis of scanning electronic microscopy images of carbonates[J].Nonlin Processes Geophys,2011,18:941-953.
[26]KWASNY W,MIKUA J.Fractal and multifractal characteristics of the PVD and CVD coatings deposited onto compound tool ceramics[J].Archives of Materials Science and Engineering,2012,56(1):37-44.
[27]YAO Shanglin,QIN Shenggao,WANG Guohui,et al.Multi-fractal characteristics of the heterogeneous pore distribution of cores[C].International Conference on Computer Distributed Control and Intelligent Enviromental Monitoring,2012:424-427.
[28]GHAMISI P,COUCEIRO M S,BENEDIKTSSON J A,et al.An efficient method for segmentation of images based on fractional calculus and natural selection[J].Expert Systems with Applications,2012,39(16):12407-12417.
[29]SATHYA P D,KAYALVIZHI R.PSO based tsallistresholding selection procedure for image segmentation[J].International Journal of Computer Applications,2010,5(4):39-46.
[30]OMRAN,MAHAMED G H.Particle Swarm Optimization Methods for Pattern Recognition and Image Processing[D].Pretoria:University of Pretoria,2004.
[2]贾芬淑,沈平平,李克文.砂岩孔隙结构的分形特征及应用研究[J].断块油气田,1995,2(1):16-21.JIA Fenshu,SHEN Pingping,LI Kewen.Study on the fractal characteristics of sandstone pore structure and its application[J].Fault-Block Oil and Gas Field,1995,2(1):16-21.
[3]刘松玉,张继文.土中孔隙分布的分形特征研究[J].东南大学学报,1997,27(3):129-132.LIU Songyu,ZHANG Jiwen.Fractal approach to measuring soil porosity[J].Journal of Southeast University,1997,27(3):129-132.
[4]王经洲,郑晓,宛农,等.基于扫描电镜图像分析的菜籽仁饼孔隙结构分形研究[J].农业工程学报,2008,24(3):16-20.WANG Jingzhou,ZHENG Xiao,WAN Nong,et al.Fractal character of the pore structure of dehulled rapeseed cake based on scanning electron microscopy image analysis[J].Transactions of the Chinese Society of Agricultural Engineering,2008,24(3):16-20.
[5]孙军昌,周洪涛,郭和坤,等.复杂储层岩石微观非均质性分形几何描述[J].武汉工业学院学报,2009,28(3):42-46.SUN Junchang,ZHOU Hongtao,GUO Hekun,et al.Characterization of complex rock micro-heterogeneity using fractal geometry[J].Journal of Wuhan Polytechnic University,2009,28(3):42-46.
[6]彭瑞东,杨彦从,鞠杨,等.基于灰度CT图像的岩石孔隙分形维数计算[J].科学通报,2011,56(26):2256-2266.PENG Ruidong,YANG Yancong,JU Yang,et al.Computation of fractal dimension of rock pores based on gray CT images[J].Chinese Science Bulletin,2011,56(26):2256-2266.
[7]葛新民,范宜仁,邓少贵,等.基于分形理论的毛管压力和电阻率指数相关性研究[J].中国石油大学学报(自然科学版),2012,36(4):72-76.GE Xinmin,FAN Yiren,DENG Shaogui,et al.Research on correlation between capillary pressure and resistivity index based on fractal theory[J].Journal of China University of Petroleum(Edition of Natural Science),2012,36(4):72-76.
[8]ABDASSAH D,PERMADI P,SUMANTRI Y,et al.Saturation exponents derived from fractal modeling of thinsections[C].SPE 36978,1996.
[9]唐红瑛,唐仁骐.砂岩岩心孔隙结构分形特征的探讨[J].中国科学技术大学学报,2004,34(s1):69-75.TANG Hongying,TANG Renqi.Study on fractal dimensions of sandstone reservoir rock samples pore structure[J].Journal of University of Science and Technology of China,2004,34(s1):69-75.
[10]唐玮,唐仁骐,白喜俊.分形理论在油层物理学中的应用[J].石油学报,2008,29(1):93-96.TANG Wei,TANG Renqi,BAI Xijun.Application of fractal dimension theory to reservoir physics[J].Acta Petrolei Sinica,2008,29(1):93-96.
[11]ESSEX,CHRISTOPHER,NERENBERG,et al.Fractal dimension:limit capacity or hausdorff dimension?[J].American Journal of Physics,1990,58(10):986-988.
[12]HARGIS C D,BISSONETTE J A,DAVID J L.The behavior of landscape metrics commonly used in the study of habitat fragmentation[J].Landscape Ecology,1998,13(3):167-186.
[13]HARGROVE W W,HOFFMAN F M,SCHWARTZ P M.A fractal landscape realizer for generating synthetic maps[J].Conservation Ecology,2002,6(1):2.
[14]孙霞,吴自勤,黄畇.分形原理及其应用[M].合肥:中国科学技术大学出版社,2003.
[15]PATRICIA Tang,NORA Y K Chew,HAK K Chan,et al.Limitation of determination of surface fractal dimension using N2adsorption isotherms and modified Frenkel-HalseyHill theory[J].Langmuir,2003,19:2632-2638.
[16]BREWER J,DI Girolamo L.Limitations of fractal dimension estimation algorithms with implications for cloud studies[J].Atmospheric Research,2006,82(1/2):433-454.
[17]曹汉强,朱光喜,李旭涛,等.多重分形及其在地形特征分析中的应用[J].北京航空航天大学学报,2004,30(12):1182-1185.CAO Hanqiang,ZHU Guangxi,LI Xutao,et al.Multi-fractal and its application in terrain character analysis[J].Journal of Beijing University of Aeronautics and Astronautics,2004,30(12):1182-1185.
[18]成秋明.非线性成矿预测理论:多重分形奇异性-广义自相似性-分形谱系模型与方法[J].地球科学:中国地质大学学报,2006,31(3):337-348.CHENG Qiuming.Singularity-generalized self-similarityfractal spectrum(3S)models[J].Earth Science:Journal of China University of Geosciences,2006,31(3):337-348.
[19]王志敬,成秋明.P-A分形模型定量度量糜棱岩变形过程中石英微结构的变化[J].地球科学:中国地质大学学报,2006,31(3):361-365.WANG Zhijing,CHENG Qiuming.Characterization of micro-texture of quartz myionite deformation process using fractal P-A model[J].Earth Science:Journal of China University of Geosciences,2006,31(3):361-365.
[20]VAZQUEZ E V,FERREIRO J P,MIRANDA J.Multifractal analysis of pore size distributions as affected by simulated rainfall[J].Vadose Zone Journal,2008,7(2):500-511.
[21]PAZ Ferreiro J,VIDAL Vázquez E.Multifractal analysis of Hg pore size distributions in soils with contrasting structural stability[J].Geoderma,2010,160(1):64-73.
[22]GARCIA Gutierrez C,SAN Jose F.Multifractal analysis of soil micro and macroporosity using digital images obtained with fluorescent dye[J].Geophysical Research Abstracts,2006,8:11094.
[23]SAN Jose Martinez F,MARTIN M A,CANIEGO F J,et al.Multifractal analysis of discretized X-ray CT images for the characterization of soil macropore structures[J].Geoderma,2010,156(1/2):32-42.
[24]ZHOU H,PERFECT E,LU Y Z,et al.Multifractal analysis of grayscale and binary soil thin section images[J].Fractals-Complex Geometry Patterns and Scaling in Nature and Society,2011,19(3):299-309.
[25]JOUINI M S,VEGA S,MOKHTAR E A.Multiscale characterization of pore spaces using multifractals analysis of scanning electronic microscopy images of carbonates[J].Nonlin Processes Geophys,2011,18:941-953.
[26]KWASNY W,MIKUA J.Fractal and multifractal characteristics of the PVD and CVD coatings deposited onto compound tool ceramics[J].Archives of Materials Science and Engineering,2012,56(1):37-44.
[27]YAO Shanglin,QIN Shenggao,WANG Guohui,et al.Multi-fractal characteristics of the heterogeneous pore distribution of cores[C].International Conference on Computer Distributed Control and Intelligent Enviromental Monitoring,2012:424-427.
[28]GHAMISI P,COUCEIRO M S,BENEDIKTSSON J A,et al.An efficient method for segmentation of images based on fractional calculus and natural selection[J].Expert Systems with Applications,2012,39(16):12407-12417.
[29]SATHYA P D,KAYALVIZHI R.PSO based tsallistresholding selection procedure for image segmentation[J].International Journal of Computer Applications,2010,5(4):39-46.
[30]OMRAN,MAHAMED G H.Particle Swarm Optimization Methods for Pattern Recognition and Image Processing[D].Pretoria:University of Pretoria,2004.